Open AccessEnergy Transportation In One‐ and Two‐Dimensional Scattering Media: Analytic Solutions of the Multiple Isotropic Scattering Model
Author(s) -
Sato Haruo
Publication year - 1993
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1993.tb01443.x
Subject(s) - isotropy , scattering , laplace transform , fourier transform , mathematical analysis , transformation (genetics) , physics , space (punctuation) , scattering theory , computational physics , mathematics , optics , computer science , biochemistry , chemistry , gene , operating system
Summary Envelopes of high‐frequency seismic waves are well described by the incoherent sum of scattered waves by heterogeneities in the earth medium. Supposing multiple isotropic scattering by point‐like scatterers randomly distributed in one‐ and two‐dimensional infinite scattering media, we derive analytic solutions for the space‐time distribution of the energy density for an impulsive isotropic radiation based on the energy transportation theory. the analytic solution obtained in two‐dimensional space coincides with that of Shang & Gao (1988). Here we show an alternative derivation of analytic solutions by using the Laplace transformation in time and the Fourier transformation in space.